Ranges of operators and Derivatives

[EN] We show a unified method of proving the existence of C(1)-Frechet smooth and Lipschitz mappings which are surjective or whose range of the derivative contains the whole dual unit ball. As an application, under Martin's Maximum axiom, we obtain a complete result for those spaces with density character omega(1). (C) 2009 Elsevier Inc. All rights reserved.Research supported by Project MTM2008-05396 and the Universidad Politecnica de Valencia. Research supported by the grants A100190502, IAA 100190801 and Inst. Research Plan AV0Z10190503. Research supported by Project MTM2008-03211 and the Universidad Politecnica de Valencia.Guirao Sánchez, AJ.; Hájek, P.; Montesinos Santalucia, V. (2010). Ranges of operators and Derivatives. Journal of Mathematical Analysis and Applications. 367(1):29-33. https://doi.org/10.1016/j.jmaa.2009.12.010S2933367

Weakly Compact Generating and Shrinking Markusevic Bases

2000 Mathematics Subject Classification: 46B30, 46B03.It is shown that most of the well known classes of nonseparable Banach spaces related to the weakly compact generating can be characterized by elementary properties of the closure of the coefficient space of Markusevic bases for such spaces. In some cases, such property is then shared by all Markusevic bases in the space

Robust Estimators in Generalized Pareto Models

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.Comment: 26pages, 6 figure

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

An Empirical Comparison of the Anova F-Test, Normal Scores Test and Kruskal-Wallis Test Under Violation of Assumptions

The present research compares the ANOVA F-test, the Kruskal-Wallis test, and the normal scores test in terms of empirical alpha and empirical power with samples from the normal distribution and two exponential distributions. Empirical evidence supports the use of the ANOVA F-test even under violation of assumptions when testing hypotheses about means. If the researcher is willing to test hypotheses about medians, the Kruskal-Wallis test was found to be competitive to the F-test. However, in the cases investigated, the normal scores test was not consistently better than the F-test or the Kruskal-Wallis test and could not be recommended on the basis of this research.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Bortezomib, Melphalan, and Dexamethasone for Light-Chain Amyloidosis

PURPOSE: Oral melphalan and dexamethasone (MDex) were considered a standard of care in light-chain (AL) amyloidosis. In the past decade, bortezomib has been increasingly used in combination with alkylating agents and dexamethasone. We prospectively compared the efficacy and safety of MDex and MDex with the addition of bortezomib (BMDex). METHODS: This was a phase III, multicenter, randomized, open-label trial. Patients were stratified according to cardiac stage. Patients with advanced cardiac stage (stage IIIb) amyloidosis were not eligible. The primary end point was hematologic response rate at 3 months. This trial is registered with ClinicalTrials.gov identifier NCT01277016. RESULTS: A total of 109 patients, 53 in the BMDex and 56 in the MDex group, received ≥ 1 dose of therapy (from January 2011 to February 2016). Hematologic response rate at 3 months was higher in the BMDex arm (79% v 52%; P = .002). Higher rates of very good partial or complete response rates (64% v 39%; hazard ratio [HR], 2.47; 95% CI, 1.30 to 4.71) and improved overall survival, with a 2-fold decrease in mortality rate (HR, 0.50; 95% CI, 0.27 to 0.90), were observed in the BMDex arm. Grade 3 and 4 adverse events (the most common being cytopenia, peripheral neuropathy, and heart failure) were more common in the BMDex arm, occurring in 20% versus 10% of cycles performed. CONCLUSION: BMDex improved hematologic response rate and overall survival. To our knowledge, this is the first time a controlled study has demonstrated a survival advantage in AL amyloidosis. BMDex should be considered a new standard of care for AL amyloidosis

A randomized phase III study of carfilzomib vs low-dose corticosteroids with optional cyclophosphamide in relapsed and refractory multiple myeloma (FOCUS)

This randomized, phase III, open-label, multicenter study compared carfilzomib monotherapy against low-dose corticosteroids and optional cyclophosphamide in relapsed and refractory multiple myeloma (RRMM). Relapsed and refractory multiple myeloma patients were randomized (1:1) to receive carfilzomib (10-min intravenous infusion; 20 mg/m(2) on days 1 and 2 of cycle 1; 27 mg/m(2) thereafter) or a control regimen of low-dose corticosteroids (84 mg of dexamethasone or equivalent corticosteroid) with optional cyclophosphamide (1400 mg) for 28-day cycles. The primary endpoint was overall survival (OS). Three-hundred and fifteen patients were randomized to carfilzomib (n=157) or control (n=158). Both groups had a median of five prior regimens. In the control group, 95% of patients received cyclophosphamide. Median OS was 10.2 (95% confidence interval (CI) 8.4-14.4) vs 10.0 months (95% CI 7.7-12.0) with carfilzomib vs control (hazard ratio=0.975; 95% CI 0.760-1.249; P=0.4172). Progression-free survival was similar between groups; overall response rate was higher with carfilzomib (19.1 vs 11.4%). The most common grade ⩾3 adverse events were anemia (25.5 vs 30.7%), thrombocytopenia (24.2 vs 22.2%) and neutropenia (7.6 vs 12.4%) with carfilzomib vs control. Median OS for single-agent carfilzomib was similar to that for an active doublet control regimen in heavily pretreated RRMM patients